Is it possible to store more than 100 MB in the browser between sessions?

Yes!

As mentioned in the comments as well IndexedDB is the way to go. PouchDB has a nice FAQ about the storage limits between different browsers.

Though Firefox has no upper limit besides disk space, if your application wishes to store more than 50MB locally [In IndexedDB], Firefox will ask the user using a non-modal dialog to confirm that this is okay.

Android works the same as Chrome as of 4.4+ (IndexedDB), while older versions can store up to 200MB (WebSQL).

And from the Chrome webpage.

Temporary storage is shared among all web apps running in the browser.{#It is also shared across all offline APIs, such as App Cache, IndexedDB, and File System. However, it does not include web storage APIs like Local Storage and Session Storage, which still has a limit of 5 MB per origin.#} The shared pool can be up to 1/3 of the of available disk space. Storage already used by apps is included in the calculation of the shared pool; that is to say, the calculation is based on (available storage space + storage being used by apps) * .333 .Each app can have up to 20% of the shared pool. As an example, if the total available disk space is 60 GB, the shared pool is 20 GB, and the app can have up to 4 GB. This is calculated from 20% (up to 4 GB) of 1/3 (up to 20 GB) of the available disk space (60 GB).